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Archimedes' Lemmas
Semicircle
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By Antonio Gutierrez
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Problem 641. Archimedes' Book of Lemmas: Proposition 2.
Level: High School, SAT Prep, College geometry. Let AB be the diameter of a semicircle, and let the tangents to it at B and at any other point D on it meet in C. If now DE be drawn perpendicular to AB, and if AC, DE meet in F, then
F is the midpoint of DE.
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